If you could capture that photon with a photovoltaic to trip a switch that kicks off a Rube Goldberg machine—isn’t that an effect?

Yes, that's an effect, just like capturing the photon and using it to build up an image is an effect. You're thinking along the wrong axis, though. The issue isn't "effect" vs "no effect". The issue is "then" vs "now".

The light that we see today left them 10 billion years ago. Any light that leaves them now[1] will never reach us. And any light emitted by us now will never reach them.

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[1] Yes, I know, "now" is not really a useful concept when dealing with large velocities in Special Relativity. I don't think my overall point is destroyed by that, though. If you can find a more rigorous way to state what I am trying to say, please do.

I think "now" is an underrated concept in physics, as in a universal ordering of events, regardless of what order position and relative velocity cause them to be observed. If there is indeed a universal "now", then faster-than-light travel need not lead to time travel.